EXCHANGE 


"A 


The  Radiating  Potentials  of 
Nitrogen 


HENRY  DEWOLF  SMYTH 


vK 


The  Radiating  Potentials  of 
Nitrogen 


A  DISSERTATION 

PRESENTED  TO  THE 

FACULTY  OF  PRINCETON  UNIVERSITY 

IN  CANDIDACY  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 

BY 
HENRY  DEWOLF  SMYTH 


Reprinted  from 
(THE  PHYSICAL  REVIEW,  N.  S.,  Vol.  XIV.,  No.  5,  November,  1919.) 


Accepted  by  the  Department  of  Physics 
June  1921 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 


•  *  »*  •  «**"/!' 


Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  XIV^N^o,,  yv  Noveipj&t, 


THE   RADIATING   POTENTIALS   OF   NITROGEN. 

BY  H.  D.  SMYTH. 

SYNOPSIS. 

1.  A  formula  is  derived  by  which  accurate  corrections  allowing  for  the  distribution 
of  velocities  of  the  impacting  electrons  may  be  applied  to  the  observed  values  of  the 
radiating  potentials. 

2.  Measurements  on  nitrogen  revealed — 

(a)  a  very  strong  effect  at  8.29  ±  0.04  volts. 

(&)  a  very  doubtful  effect  at  7.3  volts. 

(c)  an  effect  appearing  only  at  lower  pressures  but  strongly  at  6.29  ±  .06  volts. 

3.  These  results  are  explained  as  follows: 

(a)  The  wave-length  X  corresponding  to  8.29  ±  .04  is  1490.7  ±  10  and  this  effect 
is  .therefore,  identified  with  the  doublet  found  by  Lyman  at  1492.8  and  1494.8. 

(6)  This  gives  X  =  1700  and  may  be  identified  with  the  second  doublet  1742.7  and 
1745.3  attributed  to  nitrogen  but  by  some  thought  due  to  silicon. 

(c)  The  value  X  =  1965  ±  20  from  6.29  ±  .06  volts  is  taken  to  correspond  to  the 
beginning  of  the  band  spectrum  at  1870.9.  The  discrepancy  is  attributed  to  the  pres- 
ence of  nitrous  oxide. 

According  to  another  theory  the  effect  at  6.29  is  considered  due  to  lines  in  the  region 
2,000-3,000  A.U.  coming  from  neutral  atoms.  The  value  6.29  in  this  case  is  taken  as 
the  speed  necessary  before  the  electrons  can  split  up  the  molecules. 

4.  From  3  (a)  assuming  line  spectra  to  come  from  atoms,  we  have  as  an  upper 
limit  to  the  heat  of  dissociation  of  a  gram  molecule  of  nitrogen  190,000  calories. 

From  the  second  theory  in  3  (&)  we  have  as  a  possoible  actual  value  for  this  heat  of 
dissociation  145,000  calories. 

5.  Qualitative  evidence  was  obtained  supporting  Davis  and  Goucher's  discovery 
of  true  ionization  in  the  neighborhood  of  18  volts. 

I.   INTRODUCTION. 

THE  substances  whose  minimum  radiating  and  ionizing  potentials 
have  been  investigated  fall  naturally  into  two  classes,  first,  the 
monatomic  gases  and  metallic  vapors,  in  which  collisions  below  a  certain 
velocity  are  elastic,  and  second,  the  diatomic  gases,  in  which  collisions 
at  all  velocities  are  inelastic  or  at  least  partially  so,  as  in  the  case  of 
hydrogen.  . 

The  investigations  for  substances  of  the  first  class  have  recently  been 
summarized  and  discussed  by  McClennan.1  The  conclusions  drawn  are, 
briefly,  as  follows.  A  vapor,  when  bombarded  by  electrons  of  velocity 
V  emits  a  radiation  eV  =  hv.  The  first  radiation  produced  is  the  line 

1  J.  C.  McClennan,  "The  Origin  of  Spectra,"  Proc.  London  Phys.  Soc.,  XXXI.,  Part  I., 
pp.  1-29,  1918. 

44472,3 


4IS  H.    D.    SMYTH. 

at  the  head  of  the  single  t  principal  series,  and  thereafter  shorter  and 
shorter  wave-length  radiations  set  in  as  the  bombarding  electrons  attain 
correspondingly  higher  velocities.  Finally,  when  the  speed  of  the  elec- 
trons reaches  a  value  corresponding  to  the  frequency  v  =  (1.5,  S),  the 
convergence  frequency  of  the  singlet  principal  series  of  the  element  in 
question,  ionization  occurs. 

For  diatomic  gases  the  mechanism  of  ionization  or  the  production  of 
radiation  is  obviously  more  complicated  than  where  only  a  single  atom 
is  involved.  Either  it  is  necessary  first  to  dissociate  the  molecules  and 
then,  by  a  second  impact,  to  cause  radiation  or  ionization,  or  only  one 
collision  is  necessary.  .Again,  if  the  effect  is  the  result  of  one  impact, 
it  may  occur  in  two  ways;  an  electron  may  be  displaced  and  the  molecule 
broken  up  simultaneously,  or  an  electron  may  be  displaced  without 
affecting  the  bond  between  the  atoms. 

Possibly  as  a  result  of  the  above,  the  spectra  of  the  diatomic  gases 
are  very  complex  and,  for  the  most  part,  not  resolved  into  series.  This 
makes  the  prediction  of  ionizing  and  radiating  potentials  difficult.  An- 
other source  of  error  especially  serious  in  the  case  of  diatomic  gases  arises 
from  the  uncertainty  in  applying  the  necessary  correction  for  velocity 
distribution,  as  discussed  later  in  the  paper. 

In  consequence  of  these  complications,  although  values  of  the  ionizing 
and  radiating  potentials  have  been  determined  for  a  number  of  different 
diatomic  elements  and  compounds,  little  has  been  accomplished  toward 
connecting  them  with  the  spectra.  In  spite  of  the  simple  structure  of 
the  hydrogen  molecule  and  the  extensive  data  on  the  spectrum  avail- 
able, the  experimental  results  obtained  have  not  yet  been  reconciled 
with  those  predicted  by  Bohr's  theory  or  by  the  quantum  relation1 
eV  =  hv. 

Though  the  spectrum  of  nitrogen  has  not  been  resolved  into  series,  in 
the  region  of  the  ultra-violet  with  which  we  are  concerned  the  line 
spectrum  is  very  simple.  Lyman,2  in  his  investigation  of  the  extreme 
ultra-violet,  found  for  nitrogen  no  lines  except  two  doublets,  one  con- 
sisting of  the  lines  1492.8  and  1494.8  and  the  other3  of  the  lines  1742.7 
and  1745.3.  Applying  the  quantum  relation  to  these,  we  have  for  the 
corresponding  radiating  potentials,  8.28  and  8.27,  and  7.04  and  7.08 
volts.  The  longest  wave-length  of  the  band  spectrum  which  Lyman 
found  in  this  region  is  1870.9  corresponding  to  6.6  volts.  Now  the 
generally  accepted  value  for  the  radiating  potential  of  nitrogen  is  7.5 

1  Bergen  Davis  and  F.  S.  Goucher,  PHYS.  REV.,  No.  10,  p.  101,  1917. 

2  Lyman,  "  Spectroscopy  of  Extreme  Ultraviolet,"  p.  113,  1914. 
8  Possibly  due  to  silicon. 


NoL'sXIV"]  RADIATING  POTENTIALS   OF   NITROGEN.  4!  I 

volts  while  Davis  and  Goucher1  found  a  second  more  intense  radiation 
at  9  volts.2 

In  view  of  the  discrepancy  between  these  experimental  values  and  those 
calculated  from  the  spectrum,  it  was  thought  worth  while  to  attempt  a 
more  exact  determination. 

II.  APPARATUS. 

The  apparatus  used  had  been  designed  for  a  somewhat  different  purpose 
but  was  found  fairly  satisfactory. 

As  shown  in  Fig.  I,  it  consisted  of  a  glass  tube  1.5"  in  diameter,  with 
a  filament  F  sealed  in  at  one  end,  a  gauze  G  in  the  middle  and  a  disc  P 
sealed  in  from  the  other  end,  all  of  platinum.  Electrical  connections 


Ji 


Fig.  1. 

were  so  arranged  that  the  electrons  coming  off  from  the  hot  filament  F 
were  accelerated  by  a  field  between  F  and  G  but  met  a  stronger  retarding 
field  between  G  and  P.  The  difference  between  accelerating  and  retard- 
ing fields  remained  constant.  The  gauze  G  was  connected  to  a  Leeds  & 
Northrup  high  sensitivity  galvanometer  which  measured  the  electronic 
current  between  F  and  G.  The  disc  P  was  connected  to  a  Dolazalek 
electrometer  of  sensitivity  about  3,000  millimeters  per  volt,  making  the 
capacity  of  the  electrometer  system  of  the  order  of  magnitude  of  50  cm. 
The  potentials  were  read  on  a'Robt.  W.  Paul  voltmeter. 

By  coating  the  filament  with  barium  oxide  increased  emission  was 
obtained. 

The  pressure  in  the  apparatus  was  regulated  by  a  Gaede  pump  and 
measured  with  a  McLeod  gauge. 

Nitrogen  was  prepared  by  heating  sodium  nitrite  and  ammonium 
chloride  with  distilled  water  and  was  introduced  through  a  drying  tube. 
The  apparatus  was  evacuated  and  washed  out  several  times  with  nitrogen 
before  measurements  were  made. 

The  setting  in  of  radiation  was  detected  in  the  usual  manner  by  the 
photoelectric  effect  on  P  causing  an  increase  in  the  speed  of  deflection  of 

1  Bergen  Davis  and  F.  S.  Goucher,  PHYS.  REV.,  No.  13,  pp.  1-5,  1919. 

2  The  fact  that  these  are  radiation  effects  and  not  ionization  seems  to  have  been  proved  by- 
Davis  and  Goucher  and  is  taken  for  granted  in  this  paper. 


4I2  H.   D.   SMYTH. 

the  electrometer.  It  was  found  impossible  to  eliminate  all  zero  drift 
from  the  electrometer.  This  made  it  necessary  to  start  readings  far 
enough  below  the  break  point  to  give  a  good  zero.  The  accelerating 
potential  was  run  from  3  or  4  volts  up  to  n  or  12  and  then  down  again, 
the  intervals  between  readings  near  critical  points  being  as  small  as  .2 
of  a  volt.  The  values  going  up  and  coming  back  were  averaged.  The 
electronic  current  measured  by  the  galvanometer  was  kept  constant 
in  the  earlier  runs  by  adjusting  the  temperature  of  the  filament  but,  in 
the  later  runs,  the  temperature  of  the  filament  was  maintained  constant 
and  the  galvanometer  current  allowed  to  vary  with  the  accelerating 
potential,  thus  tending  to  accentuate  the  sharpness  of  the  break. 

III.  VELOCITY  DISTRIBUTION  CORRECTION. 

The  most  serious  source  of  error  in  experiments  of  this  type  is  due  to 
the  fact  that  the  electrons  reaching  the  gauze  will  not  all  have  exactly 
the  velocity  corresponding  to  the  accelerating  field.1  The  factors  causing 
this  trouble  are  the  potential  drop  along  the  filament,  initial  velocity  of 
emission  and,  in  the  case  of  diatomic  gases,  inelastic  impacts. 

Now,  in  the  case  of  monatomic  gases  the  elastic  impacts  make  possible 
a  very  effective  method  of  eliminating  this  error.  In  this  case,  the 
electrometer  current  rises  rapidly  as  the  accelerating  field  passes  the 
critical  value,  reaching  a  maximum  when  all  the  electrons  have  attained 
the  critical  speed,  and  then  falls  off  again  as  more  and  more  of  the  ionizing 
collisions  take  place  on  the  filament  side  of  the  gauze.  When  the 
accelerating  potential  becomes  great  enough  to  allow  two  ionizing  colli- 
sions by  one  electron  another  maximum  occurs,  and  so  on.  Thus,  by 
measuring  the  intervals  between  successive  maxima  the  true  value  of  the 
ionizing  potential  can  be  found.2 

With  diatomic  gases,  however,  this  method  is  impossible  since,  with 
every  increase  of  the  accelerating  field,  some  electrons  which  have  lost 
energy  by  inelastic  impact  will  attain  the  critical  speed  and  there  will 
be  a  continuous  increase  in  the  electrometer  current.  It  becomes  neces- 
sary, therefore,  to  actually  measure  the  velocity  of  the  electrons  coming 
across  and  then  make  a  correction. 

Franck  and  Hertz  did  this  but  felt  so  uncertain  as  to  the  right  method 
of  making  the  correction  that  they  claimed  an  accuracy  of  only  one  volt3 
for  their  results. 

Goucher4  eliminated  errors  due  to  the  potential  drop  along  the  filament 

1  J.  Franck  and  G.  Hertz,  Verb.  d.  D.  Phys.  Ges.,  15,  p.  37,  1913. 

2  J.  Franck  and  G.  Hertz,  Verh.  d.  D.  Phys.  Ges.,  16,  p.  457,  1914. 

3  J.  Franck  and  G.  Hertz,  Verh.  d.  D.  Phys.  Ges.,  15,  p.  39,  1913. 

4  F.  S.  Goucher,  PHYS.  REV.,  No.  8,  p.  561,  1916. 


NoL'SXIV']  RADIATING  POTENTIALS   OF  NITROGEN.  413 

by  introducing  an  equipotential  electron  source  consisting  of  a  platinum 
thimble  surrounding  a  tungsten  heating  element.  With  this  arrangement 
in  mercury  vapor  he  found  that  over  70  per  cent,  of  the  electrons  had 
velocities  corresponding  to  the  applied  voltage  and,  further,  that  the 
number  having  a  velocity  corresponding  to  .5  volt  greater  than  the 
applied  field  was  too  small  to  be  measured.  He  therefore  made  no 
correction  for  velocity  distribution.  In  the  later  work  of  Davis  and 
Goucher1  on  nitrogen,  the  same  type  of  electron  source  was  used  and 
the  correction  considered  unnecessary.  As  before  stated  the  values 
obtained  were  7.5  and  9  volts. 

Bishop,2  working  with  a  filament,  took  the  point  of  maximum  slope  of 
his  electron  current  curve  for  his  velocity  distribution  correction.  That 
is,  he  took  the  most  probable  velocity  of  the  electrons.  He  found  the 
value  of  7.5  volts  for  nitrogen  and  the  same  for  N2O. 

Hughes  and  Dixon,3  who  obtained  the  values  7.7  volts  for  nitrogen 
and  9.3  for  nitric  oxide,  took  as  their  velocity  correction  the  highest  speed 
detectable  on  their  velocity  distribution  curve. 

Attempts  to  apply  velocity  distribution  corrections  in  preliminary 
tests  of  the  present  apparatus  proved  that  the  methods  mentioned 
above  give  quite  different  results,  and  that  the  discrepancy  between  them 
varies  with  the  filament  temperature  and  gas  pressure.  Furthermore, 
when  correcting  by  the  method  of  Hughes  and  Dixon,  the  relative 
sensitivities  of  the  apparatus  for  radiation  and  for  velocity  distribution 
measurements  and,  also,  the  scale  to  which  the  measurements  were 
plotted  could  be  altered  so  as  to  vary  the  value  of  the  corrected  "break" 
point  by  as  much  as  a  volt,  without  any  obvious  way  of  selecting  the 
correct  value  from  among  the  various  possible  ones. 

This  experience  led  to  a  closer  study  of  the  problem  with  a  view  of 
determining  the  method  of  handling  data  from  the  two  types  of  measure- 
ment which  would  give  the  most  nearly  correct  result.  The  variation 
of  zero  drift  sets  a  practical  limit  to  the  scale  of  plotting  of  either  curve. 
Therefore,  it  remains  to  determine  an  appropriate  scale  for  the  more 
sensitive  measurement  and  this  is  done  by  finding  the  relation  between 
the  sensitivities  of  the  apparatus  for  the  two  types  of  measurement. 
Obviously,  the  "break"  point  in  the  radiation  curve  is  due  to  the  radia- 
tion from  the  smallest  number  of  electrons  which  can  produce  a  large 
enough  radiation  effect  to  be  detected  by  the  apparatus.  Since  not  all 
electrons  capable  of  producing  radiation  do  so,  owing  to  failure  to  collide 
or  for  other  reasons,  this  "smallest"  number  of  electrons  is  larger  than 

1  Bergen  Davis  and  F.  S.  Goucher,  PHYS.  REV.,  No.  13,  p.  i,  1919. 

2  F.  M.  Bishop,  PHYS.  REV.,  No.  10,  p.  244,  1917. 

8  A.  LI.  Hughes  and  A.  A.  Dixon,  PHYS.  REV.,  No.  10,  p.  495,  1917. 


H.    D.    SMYTH. 


FSE  COND 

[SERIES. 


G 

E 

p 

^T 

xt 

p     *' 

A 

the  least  number  which  can  be  detected  if  they  are  permitted  to  strike 
the  receiving  electrode,  as  in  the  velocity  distribution  measurements. 
The  problem,  therefore,  is  to  find  how  many  electrons  must  pass  the 
gauze  with  sufficient  energy  to  cause  radiation  in  order  that  one  may 
produce  radiation.  In  other  words,  how  many  times  less  sensitive  is  the 

apparatus  for  radiation  than  for  ve- 
locity distribution  measurements  and 
how  should  the  latter  be  plotted  in 
order  that  the  greatest  velocity  shown 
should  give  the  correction  appropriate 
to  the  "break"  point  in  the  former? 

The  following  analysis  leads  to  a 
very  usable  expression   for  the  ratio 
of  the  sensitivity  of  the  electrometer 
Fig.  2.  system  for  radiation  to  that  for  veloc- 

ity distribution  experiments. 
Let: 

N  =  number  of  collisions  per  centimeter  path  at  I  mm.  pressure; 
XA  and  XR  =  the  electric  intensities  in  the  accelerating  and  retarding 

fields,  respectively; 
n  =  number  of  electrons  per  unit  time  reaching  the  gauze  G 

from  the  filament  side; 
f(V)dV  =  the  probability  of  an  electron  reaching  the  gauze  with  a 

speed  between  V  and  V  +  d  V\ 
VQ  =  the  minimum  radiating  velocity ; 

A  and  B  be  two  planes  parallel  to  G  distant  d  and  d'  on  either  side  of 
it,  where 

V-  V0 


d  = 


and 


d' 


V-VG 
XR 


-  the  probability  of   an  electron  reaching  A  with  velocity 
between  F0  and  VQ  +  d.V. 

In  all  cases,  velocities  are  expressed  in  terms  of  equivalent  volts. 
Evidently 

nf(V0)dV(i  -  e-»Nd)  =  n(^Nd  -  i)f(V)dV 

is  the  number  of  electrons  which  pass  A  with  velocities  between  Fo  and 
VQ  +  dV  and  collide  before  reaching  G. 
After  passing  the  gauze  the  electrons  will  go  a  distance 

d'  =  (V  -  V0)JXS 


NoL'SXIV']  RADIATING  POTENTIALS   OF   NITROGEN.  415 

before  losing  their  ability  to  cause  radiation.     From  these  we  have 

nf(V)dV(i  -  e-*>Nd>) 

as  the  number  of  radiating  impacts  after  passing  the  gauze  by  electrons 
which  reached  the  gauze  with  speeds  between  V  and  V  +  d  V. 

We  have,  then,  for  the  total  number  of  impacts  at  a  speed  greater  than 
VQ,  by  electrons  going  in  the  direction  away  from  the  filament, 


- 
(eP     *A    -eP     **)f(V)dVt  (l) 

where  Vm  is  the  maximum  speed  of  any  electron  reaching  G. 

There  will  also  be  a  small  number  of  electrons  which  will  go  through, 
be  stopped,  and  acquire  sufficient  acceleration  in  the  opposite  direction 
to  produce  radiation.  For  these  we  have 


as  the  number  which  do  not  collide  before  their  velocity  is  retarded  to 
and 


ne 


»v2F° 

'~P 


as  the  number  which  will  regain  a  velocity  VQ  in  the  opposite  direction 
before  collision. 
Then 


is  the  number  which,  having  passed  G  with  velocity  between  V  and 
V  +  dV,  escape  collision  until  they  have  reversed  their  direction  and 
regained  a  speed  greater  than  V0,  finally  colliding  before  their  speed  is 
again  reduced  to  VQ. 

On  substitution  we  have 

dM2  =  n'e~pN^(i  - 

2F0 


Therefore 

Xrm  TF+FO                /  2F     v— FO\ 

[c  XR    —  e       *x*      XA    ]f(V)dV                    (3) 
0 

is  the  number  of  collisions  by  electrons  coming  in  the  reverse  direction 
and  colliding  while  they  have  a  velocity  between  Fm  and  VQ. 

We  have,  for  the  total  number  of  collisions  by  electrons  having  veloci- 
ties greater  than  VQ, 


41  6  H.   D.   SMYTH. 


V°  (A} 

XVm          —      V— —  (    ZV          V~V<>\  ^T/ 

-0 

Now  if  we  take  the  probability  of  the  production  of  radiation  and  its 
detection  by  photoelectric  effect  to  be  ( F  —  V0)/k  F0,  where  the  value 
of  k  Fo  may  be  found  from  the  results  of  Johnson1  we  have  for  the  effective 
number  of  radiating  impacts  when  the  maximum  electronic  speed  is  FTO, 

M'  = 


We  now  turn  to  the  velocity  distribution  measurements.  If  D  is 
the  distance  from  the  gauze  G  to  the  plate  P  and  VR  is  the  retarding 
potential,  the  number  of  electrons  getting  to  the  plate  will  be,  for  given 
values  of  Vm  (i.e.,  VA,  the  accelerating  potential)  and  VR, 

(6) 

Now,  the  form  of  the  function  /( F)  will  vary  with  Vm  (or  VA)  and  its 
value  will  depend  also  on  the  particular  value  of  F  substituted. 
For  a  given  value  of  Vm  we  will  have,  from  (6), 

(7) 

Consider  the  part  near  the  foot  of  a  typical  velocity  distribution 
curve,  as  shown  by  Fig.  3.  The  curve  is  a  section  of  a  parabola,  while 
actual  experimental  measurements  are  indicated  by  dots.  It  is  evi- 
dently sufficiently  accurate,  for  the  present  purposes,  to  consider  the 
lowest  part  of  the  distribution  curve  to  be  parabolic,  so  that  its  slope 
is  taken  to  be  proportional  to  the  horizontal  distance  from  the  foot. 
Use  of  this  property  gives  the  graph  shown  in  Fig.  4. 

Let  VR>  be  some  particular  value  of  VR ;  then 


l=¥R' 

Also,  we  have,  for  any  value  of  VR  less  than  FTO, 

dMP  _Vm-VR  (dMP 
dVR  "  Vm  -  F 

1  J.  B.  Johnson,  PHYS.  REV.,  X.,  p.  609,  1917. 


NoL6XIV'j                      RADIATING  POTENTIALS   OF   NITROGEN. 

Combining  these  two  equations,  we  have 

(MP)VK.  - 

2     Fw  -  VR 

dVR 

O.4-.0         \       .1 

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II                 '\         -  ft; 

)      •  <-     rrv  pt—^tT,  fc  -  __  u.  - 

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WCily  JiSLTLDU.  .Ipn 

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G.0.0                     "V       — 

ruro.Pt  to.  j     .      ! 

• 

T 

— 

g 

"*            lj~  .-  f  IL 

(ylfll.x^f|=D. 

Jifi^l 

J 

«  «  c                       V     ! 

ok-Mp  =.  OJ364 

Pg* 

P^  2.0              . 

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il=  £_  'QJ-ff 

O               ~    '-  .  •  -    -.-  -   •            V 

J      -  ;:       i         ^ 

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l    -•!               i 

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»-2j  0.5 

-  -  ^ 

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LU              i  ••.:-•• 

•  •••  v 

1     >^     ' 

O.C      ! 

417 


•u    -/.o    -0.8    -as    -0.4   -0.2   -o.o 

Fig.  3. 

Substituting  for  dMP/dVR  from  (7),  and  solving  for  f(V)v=VR,  we  have 

2(MP)F/FTO  - 


*(Vm  ~  V*? 
We  are  endeavoring  to  find  the  ratio  of  corresponding  values  of  M' 


10 

8 

4- 
0 

\ 

1     | 

- 

1 

E 

A^ 

7^/r 

P 

A  ! 

\ 

Ifi 

Y 

c 

0 

br 

?a' 

•  r-j- 

q 

/ 

rr/tr 

p 

&  Pa 

rfl 

: 

s 

"ft 

n: 

re 

1 

\ 

i 

^ 

J 

\ 

— 

V 

K 

; 

• 

r 

j 

j 

| 

| 

\ 

| 

- 

• 

\ 

V 

I 

i 

\ 

i 

. 

\ 

- 

1 

S  : 

• 

. 

—  fi^l 

. 

< 

- 



1 

/\ 

n' 

i    IV 

1 

\ 

• 

1 

, 

\ 

1 

4rf 

CL= 

My>) 

\ 

Li 

*•    ' 

H 

\ 

, 

'•• 

\ 

i 

: 

1 

4 

I 

• 

V 

, 

^ 

- 

^L']"" 

--- 

4,S        '  5.0 

I      i2 

5^- 

56 

,*? 

5£ 

&0 

*•* 

Fig.  4. 


41  8  H.    D.    SMYTH. 

and  MP,  i.e.,  of  values  at  equal  distances  from  the  break  point.  For 
this  condition  we  must  have 

Vm  -  Fo  =  Vm  -  VR, 

and  ( V  —  Fo)  in  the  case  of  radiation  corresponds  to  ( Vm  —  VR)  in 
the  velocity  distribution.  We  can  therefore  substitute  the  value  found 
above  for/(F)  in  the  expression  for  M'  if  we  write  Vm  —  VQ  for  Vm  —  V R 
and  V  —  VQ  for  Vm  —  VR.  If  at  the  same  time  we  divide  through  by 
(MP}vRl,  we  have  the  following  expression  for  the  required  ratio: 


Mr  C 

IF  =  2<pm  \ 

Mp  Jv, 


(Vm    -     F0)2  kV0 


for  corresponding  values  of  Mr  and  MP  in  the  neighborhood  of  the  break 
point. 

If,  in  the  above  expression,  we  put  the  constant  factors  outside  the 
integral  and  set  pN/XA  =  a,  pN/XR  =  a'  and  F  —  F0  =  x,  and  if  we 
take  a  =  a',  which  is  very  nearly  true  we  have 

M1  2€pND 


CXm 

I         X2\€ax   —   €~ax  4- 
F  L  ' 

Jo 


K/T  J,  T7  /  T7  T7 

Mp          kVQ(Vm—    V  o 

By  integration  and  the  expansion  of  the  powers  of  e  (either  before  or 
after  integration),  this  equation  takes  the  following  form,  which  includes 
all  terms  as  far  as  those  in  a3: 


+  -V-a2F0(Fw  -  Fo)  +  2a2F02  +•••]. 

Practically,  the  terms  in  a2  are  negligible,  since  a  is  of  the  order  of  magni- 
tude of  0.03. 

If,  therefore,  we  call  the  sensitivity  of  the  apparatus  for  radiation  R 
and  for  velocity  distribution  S,  we  have,  for  practical  purposes, 


R      _M'_      e»NDa(Vm-  F0)2/ 
S  ~ioMm~  ' 


where  Vm  is  the  maximum  speed  detectable  in  velocity  distribution 
measurements  and  the  factor  i/io  is  introduced  because,  in  our  apparatus, 
the  dimensions  were  such  that  P  receives  only  about  that  proportion 
of  the  radiation  starting  at  the  gauze. 

Equation   (8)   is  evidently  not  exact,   owing  to  the  approximations 


VOL.  XIV. 
No.  5. 


RADIATING   POTENTIALS   OF   NITROGEN. 


419 


introduced  in  order  to  obtain  a  solution.  It  is  believed,  however,  that 
none  of  these  approximations  is  seriously  in  error,  so  that  the  results 
given  by  (8)  should  be  of  the  right  order  of  magnitude. 

The  necessary  procedure,  therefore,  is  to  plot  the  velocity  distribution 
on  the  same  scale  on  which  the  radiation  curve  is  to  be  plotted  and  deter- 
mine Vm  from  this.  Then  multiply  the  values  of  the  electrometer  current 
for  each  value  of  VR  by  the  corresponding  values  of  R/S  and  replot. 
The  break  point  in  this  new  curve  determines  the  correction  to  be  used 
on  the  radiation  curve.  The  necessity  of  plotting  a  corrected  velocity 
distribution  curve  is  made  evident  by  Table  I.  which  gives  the  values 
of  S/R  calculated  by  equation  (8)  for  different  values  of  VR  —  Vm,  taking 
k  =  2  for  nitrogen.1 

TABLE  I. 


0.015  mm- 


7-5  volts. 


fc-Fft. 

SIR. 

(p»->j& 

SIR. 

.1 

795,000 

.1 

6,500 

.3 

87,500 

.2 

5,500 

.5 

31,000 

.3 

4,700 

.6 

22,000 

.4 

4,050 

.7 

16,000 

.5 

3,500 

.8 

12,500 

.6 

3,200 

.9 

9,500 

.7 

2,750 

1.0 

8,000 

IV.   EXPERIMENTAL  RESULTS. 

It  was  found  impossible  to  eliminate  all  zero  leak  from  the  electrometer. 
Consequently  readings  had  to  be  taken  at  low  accelerating  potentials  to 
establish  a  zero  line.  Errors  due  to  a  variation  in  this  zero  leak  as  well 
as  errors  of  observation  were  pretty  well  eliminated  by  the  method  of 
taking  a  series  of  readings  with  fields  increasing  and  then  decreasing 
and  plotting  the  mean.  A  typical  set  of  readings  is  given  in  Table  II., 
below, 
where 

Vf  =  P.D.  across  filament  in  volts; 
G  =  current  to  gauze  in  amperes  X  io~8; 
T  =  time  in  seconds  for  electrometer  to  deflect  one  cm.; 
T  =  mean  of  T  and  T'  observations  as  VA  was  increased  and 

then  decreased  respectively; 

I  IT  =  rate  of  deflection  of  electrometer  in  cms.  per  second. 
The  values  of  VA  and  i/T,  that  is  the  accelerating  potential  and  the 
current  to  the  electrometer,  were  used  in  making  the  curves.     The  first 

JJ.  B.  Johnson,  loc.  cit. 


420 


H,   D.   SMYTH. 


[SECOND 
[SERIES. 


P  = 


TABLE  II. 

Observations  for  Run  No.  13. 
o.oi  mm.,     VR  —  VA  =  2.5  volts,     V/  =  0.8  volts. 


r+ 

G. 

G'. 

C 

T'. 

T. 

I  IT. 

l 

6 

6 

81 

81 

81 

.0124 

2 

16.4 

17 

79 

86 

82.5 

.0121 

3 

21.2 

21 

76 

86 

81 

.0124 

4 

23 

22 

82 

8'0 

81 

.0124 

5 

23.7 

22.4 

73 

89 

81 

.0124 

5.5 

24.1 

22.5 

71 

74 

72.5 

.0138 

5.75 

24.4 

22.4 

76 

71 

73.5 

.0136 

6 

24.7 

22.3 

66 

61 

63.5 

.0158 

6.25 

25 

22.1 

63 

60 

61.5 

.0163 

6.5 

25.2 

22.1 

60 

56 

58 

.0172 

6.75 

25.5 

21.9 

55 

55.6 

55.3 

.0181 

7 

25.8 

21.7 

50 

53 

51.5 

.0194 

7.25 

26.2 

21.6 

46.4 

45.4 

45.9 

.0218 

7.5 

26.6 

21.5 

44 

44.6 

44.3 

.0220 

7.75 

26.9 

21.3 

41 

41 

41 

.0244 

8 

27.2 

21 

35.2 

35 

35.1 

.0285 

8.25 

27.4 

21 

29.8 

30.2 

30 

.0330 

8.5 

27.7 

20.9 

23.4 

27.5 

25.5 

.0392 

8.75 

28 

20.8 

20.2 

22.1 

21.1 

.0474 

9 

28.2 

20.7 

16.8 

19.4 

18.2 

.0550 

9.5 

28.5 

20.8 

10.6 

12.5 

11.5 

.0870 

10 

28.7 

20.8 

7.5 

9.0 

8.2 

.122 

11 

29.2 

21 

1.8 

3.0 

2.4 

.417 

12 

29.5 

21.1 

.58 

.7 

.64 

1.563 

detectable  departure  from  the  zero  line  was  taken  as  the  break  point. 
Thus,  in  run  no.  4,  Fig.  5,  the  break  point  comes  at  9.3  volts.  In  order 
to  correct  this  we  examined  the  velocity  distribution  curve  for  run  no.  4 
in  Fig.  6.  Here  we  saw  that  the  uncorrected  values  (curve  a)  gave  a 
break  point  at  VR  —  VA  =  o  and  therefore  Vm  —  VA  —  o.  Using  this 
value  to  get  ( Vm  —  VR) ,  and  so  to  calculate  the  corrected  values  of  the 
current  by  applying  equation  8,  we  got  the  curve  b  which  has  its  first  break 
point  at  VR  —  VA  =  —  i.o.  We  concluded,  therefore,  that  the  first 
electrons  which  are  effective  in  producing  detectable  radiation  have  a 
velocity  one  volt  less  than  the  applied  field,  giving  us  8.3  as  the  true 
value  of  the  radiating  potential  from  this  run. 

Similarly  for  run  no.  5  we  found  the  observed  break  to  be  at  9.0  and 
the  corrected  value  to  be  8.0  volts. 


VOL.  XIV.1 
No.  S. 


RADIATING   POTENTIALS   OF  NITROGEN. 


421 


In  run  no.  6,  Fig.  7,  on  the  other  hand,  we  found  the  corrected  value 
to  come  at  6.5  (5.9  observed),  but  there  is  a  sharp  increase  in  the  slope 


in  volts 


Fig.  5.  Fig.  6. 

of  the  curve  at  8.6  (8.0  observed).     This  run  therefore  apparently  has 
two  breaks  corresponding  to  two  critical  speeds. 


r 


10 


Fig.  7. 


Fig.  8. 


422 


H.    D.    SMYTH. 


("SECOND 

[SERIES. 


In  runs  nos.  n  and  12  the  effect  at  the  lower  voltage  was  so  great  as 
to  make  it  impossible  to  detect  any  other.  For  these  runs  the  corrected 
values  are  6.15  and  6.4  volts. 

From  these  five  typical  curves  shown,  it  is  clear  there  are  two  distinct 
critical  points,  each  curve  showing  one  or  both,  more  or  less  sharply. 
The  values  observed  were  weighted  according  to  the  sureness  with  which 
the  break  point  could  be  picked.  The  velocity  distribution  curves  were 
treated  similarly  and  the  weight  of  the  corrected  value  taken  as  the 
product  of  the  weights  of  the  two  observations. 

In  Table  III.  the  results  from  the  curves  shown  and  discussed  above 
are  grouped  with  all  other  runs  which  gave  results  sufficiently  definite  to 

have  weight. 

TABLE  III. 

Experimental  Results, 


No. 

(mm.). 

G. 

Observed  Breaks  with 
Weighting. 

Corrections 
with  Weight- 
ing. 

Corrected  Breaks  with 
Weighting. 

1 

.048 

25. 

9.4    (4) 

-0.4  (3) 

8.5  (12) 

2 

.038 

25. 

9.2    (3) 

-0.9  (3) 

8.3  (9) 

3 

.027 

25. 

•9.3    (2) 

7.5    (?) 

-1.0(3) 

8.3  (6) 

4 

,015 

25. 

9.3    (3) 

-1.0(3) 

8.3  (9) 

5 

.015 

250. 

9.0    (4) 

-1.0(3) 

8.0  (12) 

6 

.015 

2500. 

8.0    (1) 

5.9    (2) 

+0.6  (3) 

8.6  (3) 

6.5    (6) 

7 

.015 

2500. 

5.4    (5) 

+0.7  (2.5) 

6.1  (8) 

8 

.045 

750. 

9.3    (2) 

-.08  (4) 

8.5  (8) 

9 

.045 

140. 

9.2     (1) 

-1.0  (4) 

8.2  (4) 

10 

.026 

250. 

8.8    (2) 

7.4    (1) 

-0.7  (5) 

8.1  (10) 

6.7    (5) 

11 

.01 

500 

4.75  (4) 

+  1.4  (3) 

6.15  (12) 

12 

.01 

2.5 

7.75  (?)        5.2    (4) 

+  1.2  (3) 

6.4    (12) 

13 

.01 

40 

6.5    (?)        4.2    (3) 

+  1.9  (3) 

6.1     (4) 

Mean  values 

8.285 
±.045 

6.285 
±.061 

Note. — Runs  7,  n  and  13  and  some  not  given  above  show  uncertain  indications  of  a  third 
break  at  about  7.4  volts;  G  is  the  electronic  current  in  amperes  X  io~9. 


V.   DISCUSSION  OF  RESULTS. 

Let  us  now  compare  the  experimental  results  just  presented  with 
Lyman's  data  on  the  spectrum  of  nitrogen  in  the  extreme  ultra-violet 
given  at  the  beginning  of  this  paper.  This  is  best  done  by  writing 
corresponding  values  opposite  each  other  in  a  table. 

I.  The  Break  at  8.29  Volts. — In  this  table  we  see  that  the  effect  which 
we  got  at  all  pressures  tried  and  with  various  currents,  that  ,is  the  most 


VOL.  XIV.1 
No.  5. 


RADIATING   POTENTIALS   OF   NITROGEN. 


423 


TABLE  IV. 


Spectrum  Data. 


Radiation  Experiment  Data. 


Remarks. 


X  (Obs.).     fb  (Calc.).        />o  (Obs.).  X  (Calc.). 


Doublet  almost  certainly  due  to  nitrogen     1492.8 

;    1494.8 


8.28        8.29  ±  .04     1490.7  d=  10 
8.27 


Doublet  attributed  to  nitrogen  but  pos- 
sibly due  to  silicon             '> 

1742.7    1 

7.08 

7.3  (?) 

1700  (?) 

1745.3 

7.09 

Beginning  of  band  spectrum  i 

1870.9 

6.6 

6.29  db  .06 

1965  ±  20 

intense  effect,  corresponds  with  greater  accuracy  than  could  be  hoped 
for,  to  the  most  certain  doublet  of  the  line  spectrum  of  nitrogen. 

2.  Possible  Effect  at  7.3    Volts. — The  failure  of  the  second  value  to 
coincide  with  that  for  the  other  doublet  is  no  greater  than  the  uncer- 
tainties of  its  determination.     This  radiation  was  apparently  the  weakest 
of  the  three  and,  while  showing  up  well  on  one  or  two  curves  was,  on  the 
whole,  rather  doubtful.     Attention  should  again  be  called  to  the  doubt 
concerning  the  origin  of  this  doublet  as  determined  by  Lyman. 

3.  Explanation  of  6.2p-Volt  Break. — Two  different  theories  were  de- 
veloped to  account  for  this  effect,  one  depending  on  the  application  of  the 
quantum  relation  to  the  band  spectrum  and  the  other  involving  the  idea 
of  dissociation  and  the  subsequent  production  of  spectral  lines.     They 
are  discussed  at  length  in  what  follows. 

(a)  To  explain  the  experimental  result  of  a  break  occurring  only  at 
low  pressures  and  coming  at  6.29  volts  instead  of  the  6.6  calculated 
from  the  band  spectrum,  we  must  consider  the  effect  of  a  probable 
impurity.  Kreusler1  found  that  nitrogen  prepared  in  a  manner  almost 
identical  with  that  used  in  the  present  experiment  had  a  small  quantity 
of  N2O  present  as  an  impurity.  He  found  that  this  increased  absorption 
at  X  =  1, 860  from  2.2  per  cent,  for  atmospheric  nitrogen  tto  14.3  per  cent. 
He  also  made  measurements  on  pure  nitrous  oxide  and  found  88.4  per 
cent,  absorption  at  X  =  2,000,  apparently  increasing  beyond  his  powers 
of  measurement  at  1,930  and  1,860. 

It  is  probable,  therefore,  that  at  the  higher  pressures,  the  radiation 
X  =  1,965  corresponding  to  6.3  volts  loses  so  much  energy  by  absorption 
in  the  I  cm.  space  between  the  gauze  and  the  plate  that  it  is  not  detect- 
able. This  explains  the  fact  that  there  was  no  trace  of  this  break  at 
pressures  above  0.026  and  that  it  was  only  detected  in  one  case  at  pres- 
sures exceeding  0.015. 

1  H.  Kreusler,  Ann.  d.  Phys.,  6,  p.  419,  1901. 


424  H.   D.   SMYTH. 

The  discrepancy  between  the  value  6.3  found  and  the  6.6  corresponding 
to  the  beginning  of  the  band  spectrum  is  not  so  easily  accounted  for. 
It  is  a  well  known  fact,  however,  that  the  presence  of  small  impurities 
greatly  affects  the  intensity  of  emission  spectra.  We  have  just  seen  that 
there  is  such  an  effect  in  the  absorption  spectrum  of  nitrogen  in  this 
region.  Is  it  not  possible  then  that  the  presence  of  N2O  may  cause  less 
refrangible  bands  up  to  X  =  1,965  to  come  out  with  sufficient  strength 
to  be  detected?  The  chances  for  sufficient  experimental  error  to  account 
for  a  discrepancy  of  0.3  volt  do  not  seem  great  especially  in  view  of  the 
extremely  good  agreement  in  the  case  of  the  highest  break.  It  is  hoped 
that  this  point  may  be  cleared  up  by  further  work  taking  every  precau- 
tion to  get  absolutely  pure  nitrogen. 

(b)  The  other  explanation  of  our  6.3  volt  break  is  quite  different. 
There  are  lines  in  the  spectrum  of  nitrogen  in  the  region  between  2,000 
and  3,000  which  would  produce  photoelectric  effect  and  the  most  re- 
frangible of  which  is  X  =  2,052.*  In  the  previous  discussion  it  has  been 
assumed  that  these  arise  from  systems  that  are  not  present  in  this 
experiment,  such  as  charged  atoms  or  molecules,  since  otherwise  we  would 
have  a  photo-electric  effect  at  lower  voltages.  If  we  allow  the  possibility 
of  the  production  of  some  of  these  lines  by  a  neutral  atom,  as  we  must 
for  the  doublet  previously  considered,  then  we  must  first  have  dissociation 
a*nd  then  a  radiating  impact.  Now  the  speed  necessary  for  an  electron 
to  produce  these  radiations  is  between  4  and  6  volts,  but  the  energy 
necessary  to  dissociate  a  nitrogen  molecule  is  unknown.  The  velocity 
necessary  for  an  electron  to  dissociate  a  hydrogen  molecule  is  found 
by  calculation  from  Langmuir's2  results  to  be  about  3.6  volts  and  it  is 
known  that  nitrogen  is  much  harder  to  dissociate.  It  is  possible  therefore 
that  6.3  is  the  speed  necessary  to  dissociate  the  molecules  and  thus  make 
it  possible  for  the  electrons  of  lower  speed  to  produce  radiation.  This 
would  correspond  to  a  heat  of  dissociation  of  a  gram  molecule  of  nitrogen 
of  145,000  calories,  whereas  Langmuir3  found  for  hydrogen  the  value 
84,000. 

This  theory  necessitates  a  new  explanation  of  the  effect  of  pressure, 
since  these  longer  wave-length  radiations  will  not  be  so  strongly  absorbed. 
It  must  be  supposed  that  the  chances  for  recombination  of  the  atoms 
at  higher  pressures  than  0.026  are  so  great  as  to  make  the  radiation 
negligibly  small. 

As  to  the  soundness  of  the  assumption  of  radiation  from  neutral  atoms, 
we  have  the  following  statement  of  J.  J.  Thomson  regarding  the  lines  of 

1  Lyman,  "Spec,  of  Extreme  Ultraviolet,"  p.  83,  1914. 

2  I.  Langmuir,  J.  of  Am.  Chem.  Soc.,  37,  pp.  417-458,  1915. 
8  Ibid.,  p.  457. 


NoL'sXIV']  RADIATING  POTENTIALS  OF' NITROGEN.  425 

the  hydrogen  spectrum:  "All  theories  concur  in  regarding  the  atom  and 
not  the  molecule  as  the  source  of  these  lines,  but  according  to  Wien's 
theory  the  atom  radiates  when  in  the  neutral  state,  while  Stark  maintains 
that  the  radiation  is  emitted  when  the  atom  has  a  positive  charge: 
according  to  his  view  the  lines  emitted  by  the  neutral  atom  are  far  away 
in  the  ultra-violet."  *  Stark2  found  no  lines  attributable  to  a  neutral 
nitrogen  atom  but  hardly  carried  his  work  below  4,000  A.U.  From  his 
work  on  mercury,  however,  he  concluded  that  the  line  2,536.7  was  due 
to  a  neutral  atom.3  It  is  evident  then  that  there  is  no  evidence  against 
our  assumption  but  rather  indications  of  its  probability. 

A  second  assumption  implied  in  this  theory  is  that  the  neutral  mole- 
cules will  not  set  up  ultra-violet  radiation  when  struck  by  electrons  with 
speeds  below  6.3.  On  this  point,  I  have  found  no  evidence. 

4.  Upper  Limit  to  Heat  of  Dissociation  of  Nitrogen. — A  necessary  con- 
sequence of  the  principle  that  the  line  spectrum  is  due  to  atomic  nitrogen 
is  the  determination  of  an  upper  limit  for  the  energy  necessary  to  dis- 
sociate a  nitrogen  molecule.  If  the  effect  resulting  rom  bombardment 
by  electrons  with  velocities  of  8.24  volts  is  due  to  atoms,  the  molecules 
must  be  dissociated  by  the  impact  of  electrons  of  this  or  lower  speed. 
The  value  8.3  would  give  as  an  upper  limit  for  the  heat  of  dissociation 
of  a  gram  molecule  of  nitrogen  about  190,000  calories.  As  has  been 
stated,  Langmuir4  found  the  value  for  hydrogen  at  constant  volume  to 
be  84,000  calories. 

VI.     lONIZATION  AT    18.5  VOLTS. 

Goucher  and  Davis  found  that  what  had  previously  been  called 
ionization  in  nitrogen  was  really  radiation  but  that  true  ionization  did 
occur  at  18.5  volts.  Although  the  apparatus  used  in  the  present  investi- 
gation was  not  well  suited  for  testing  this  point,  by  greatly  reducing 
its  sensitivity  a  distinct  increase  in  the  slope  of  the  electrometer  current 
curve  in  the  neighborhood  of  18  volts  was  observed,  thus  supporting  the 
more  accurate  work  of  Davis  and  Goucher. 

It  is  realized  that  the  present  results  were  not  obtained  under  experi- 
mental conditions  ideal  for  getting  sharp  break  points  or  reducing  cor- 
rections to  a  minimum.  The  attempt  was  made,  on  the  other  hand,  to 
employ  experimental  conditions  in  which  the  corrections  would  be  as 
varied  as  possible,  in  order  to  test  the  soundness  of  the  formula. 

1  J.  J.  Thomson,  "Positive  Rays,"  pp.  96-97,  1913. 
1  J.  Stark,  Ann.  d.  Phys.,  55,  pp.  29-74,  P-  73.  1914- 
1  J.  Stark,  Ann.  d.  Phys.,  52,  pp.  241-302,  p.  247,  1913. 
4  I.  Langmuir,  loc.  cit.,  p.  457,  1915. 


426  H.   D.    SMYTH. 

Although  the  corrections  in  different  tests  differed  by  as  much  as  3  volts 
in  extreme  cases,  the  corrected  values  of  the  break  point  were  quite  con- 
sistent. It  appears,  therefore,  that  the  above  analysis  is  justified  and 
necessary,  and  that  the  final  values  obtained  are  trustworthy. 

The  author  wishes  to  .express  his  indebtedness  to  Professor  K.  T. 
Compton,  whose  supervision  and  assistance  have  made  this  work  possible. 

PALMER  PHYSICAL  LABORATORY, 
PRINCETON,  N.  J. 
July,  1919. 


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